Modelling of E2/E2/1/m queueing system subject to breakdowns and customer rejection during failure

Abstract

The paper deals with modelling of a finite single-server queueing system with a server subject to breakdowns. Customer interarrival times and customer service times follow the Erlang distribution defined by the shape parameter k=2 and the scale parameter 2λ or 2μ respectively. It is considered that server failures can occur when the server is either idle or busy – operate-independent failures. Further it is assumed that the system empties when the server is broken (all customers are being rejected). Random variables relevant to server failures and repairs are exponentially distributed. In the paper the state transition diagram is shown, the system of linear equations describing the system in the steady state and the formulas for several performance measures computation are presented. At the end of the paper there are shown some graphical dependencies.